A new objective will trigger after completing two heroic acts in Mission 5. Very rarely, the next event won't trigger after completing Petty Crime and then Arson. If this happens, please try rebooting the game. If this does not fix the issue then the progression will need to be restarted from the beginning.
Sometimes failing to complete the Arson event will keep Mission 5 from progressing. If this happens, return to the main menu and reload the most recent save.
Web rushing to the Central Park objective in Mission 5 may cause the game to teleport you back to your original position and keeping you from progressing. If this happens, return to the main menu and reload the most recent save.